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<p>Suppose we know the value of the quantity now and we wish to predict its value in the future. This quantity can be, for example, the temperature of coffee in a cup, the number of people infected with a virus, the concentration of carbon dioxide in the atmosphere. To do the prediction, we must know how quickly these quantities are changing. Mathematically, the rate of change of one quantity is the derivative. And practically the rate of change of a quantity will depend on the quantity itself. Therefore, we may model the problem as <span class="process-math">\(\frac{\textrm{d} y}{\textrm{d} t}=f(t, y)\text{.}\)</span> This equation contains derivative, so it is a differential equation. Through this equation and the initial condition, we may know the behavior of this quantity at any time.</p>
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